On the continuum modeling of the foldable rod with rigid links

We study the small-amplitude motion of a foldable, rod-like structure consisting of rigid links connected by torsional springs. The discrete model of the structure results in two dispersion curves: acoustic and optical. Depending on the structural parameters, stop bands may be observed. Using the long-wave approximation, we introduced a series of continuum models. However, the first-order approximation does not capture the behavior of the discrete model. Interestingly, in some cases, there is only an optical mode. However, higher-order approximations can reproduce behavior similar to that of the discrete model. Therefore, the bending-dominant structure requires an enhanced continuum model.